Is it possible to change battery in iphone 4?

I want to change a battery… How much it cost?

There are different costs depending on the quality of your battery at its current standpoint, and many other factors. Yes, they can replace your battery but unless its under warranty or special insurance, it will cost money. I would suggest going to an Apple Store near you, when you can get free help and a "diagnosis" of sorts on your phone to see how much it will cost, and if you want to send it away, etc. Etc.